In the past, there have been known SOx concentration sensors arranged inside engine exhaust gas passages so as to detect the SOx concentration in the exhaust gas. These known SOx concentration sensors normally use solid electrolytes and measure the electromotive force generated by the change of SOx into sulfate ion to detect the SOx concentration in the exhaust gas (for example, see Japanese Patent Publication (A) No. 2004-239706).
However, a conventional SOx detection system using this kind of SOx concentration sensor can only operate under high temperatures and becomes bulky as an apparatus. In particular, when the SOx concentration is low, there is the large problem of not being able to detect the SOx concentration. Conventionally, as in this SOx concentration sensor, attention has only been directed at instantaneously and directly detecting the SOx concentration in the exhaust gas. So long as trying to instantaneously and directly detect the SOx concentration in the exhaust gas in such a way, various problems inevitably occur like as explained above.
Therefore, the inventors changed their way of thinking and focused not on instantaneously detecting the SOx concentration, but on detecting the cumulative amount of sulfur S over a long period. It has been proven that by changing the way of thinking in this way, it would be possible to easily estimate the amount of SOx in the exhaust gas even without directly detecting the SOx concentration in the exhaust gas.